Determine if the following theorem can be applied to show that the following functions are continuous at
Question:
Determine if the following theorem can be applied to show that the following functions are continuous at the given points.
Differentiable Implies Continuous: Let f be a real-valued function of two or three variables defined on an open neighborhood of P 0 . If f is differentiable at P 0 then f is continuous dt P 0 .
(a) f(x, y) = e 2x2 – 4y 2 , P(0, 0)
The theorem can be applied.
The theorem cannot be applied.
(b) f(x, y) = √x 2 + y 2 , P(0, 0)
The theorem can be applied.
The theorem cannot be applied.
(c) f(x, y, z) = In(1 + x2 + y2 + z2, P(4, 2, 5)
The theorem can be applied.
The theorem cannot be applied.
(d) f(x, y, z) = e x2 y 4 sin (xyz), P(3, 2, π/12)
The theorem can be applied.
The theorem cannot be applied.Probability & Statistics for Engineers & Scientists
ISBN: 978-0130415295
7th Edition
Authors: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying